By far the most common atmospheric storm is the thunderstorm. Approximately 44,000 thunderstorms occur daily over the surface of the earth, with about 2,000 in progress at any time. Because of their prevalence, as well as severity, the thunderstorm; is of primary importance. The need exists for mapping any storm having associated electrical activity, which includes tornados, snowstorms, sandstorms, and even clear air storms, which have reported electrical activity. The need for storm mapping includes:
1. Storm Avoidance,
2. Severe Storm Warning, and
3. Weather Prediction.
Storm avoidance is of great concern when traveling, and especially for air and sea travel. Warning of severe storms that may be approaching is sometimes important in order to minimize hazards to life and property. Weather prediction as related to approaching storms can be of great interest to those involved in agricultural and recreational pursuits.
We will devote our attention primarily to storm mapping and avoidance as related to air travel, since this application represents one of the greatest segments of use. The invention to be described, however, has application wherever storm detection and display mapping is needed.
Thunderstorms represent one of the greatest dangers to air travel. Such storm are characterized by turbulence, heavy rain, hail, and lightning. Turbulence is frequently so severe that there is a possibility of aircraft structural failure, causing crash. In less severe cases, passenger discomfort occurs. Hail can also cause severe damage to an aircraft, and can prove fatal. Pilots also prefer to avoid lightning and heavy rains. In summary, aircraft flight into thunderstorm regions can be perilous, and should be avoided.
The name of the thunderstorm originated from the sound produced by the storm. Since thunder is the result of lightning strokes, a thunderstorm is a storm having lightning.
There are two basic types of thunderstorms, classified according to the mechanism generating the storm. They are:
1. The Convective Thunderstorm
2. The Frontal Thunderstorm
The most common type of convective storm is caused by heating of the earth's surface by the sun. On a hot clear day, the earth's atmosphere is relatively transparent to the sun's rays, and therefore a substantial portion of the sun's radiant energy falling on the earth, heats the earth's surface. The warm layer of air near the ground starts rising, but the whole layer of air over an extensive area cannot rise simultaneously. Instead, air rises in discrete vertical channels or cells about a half mile in diameter. The cells of rising warm air are spaced in honeycomb fashion over the terrain, while in the spaces between them, colder air descends to take the place of the rising warm air.
As the warm air rises, cooling takes place. If the air contains sufficient moisture, condensation takes place, and a cumulus cloud begins to develop. If the humidity is high, these cumulus clouds continue to increase in size, with several grouping together to form even larger cloud masses. If conditions of temperature and humidity are proper, this "build up" process will continue until cloud tops are in the order of 25,000 to 40,000 feet or higher as they become fully developed storms.
This type of storm has its origin in the convective air currents from the ground, and are thus called "convective storms". These storms usually build up during the afternoon with the heat of the day, then dissipate by evening. However, there are types of convective storms that build up and occur at night especially over the sea. Convective thunderstorms are typically distributed over an area and exist as scattered groups of storm cells.
Another variety of thunderstorm is the frontal storm. Frontal thunderstorms are generated when a warm front flows into a colder air mass. The temperature gradient between the two masses of air causes the warmer air to rise. Again, if conditions of temperature and humidity are proper, the rising motion of the air will enter an unstable state called "free convection", whereby the vertical air movements gain momentum. As this process continues, cells of thunderstorms are generated in much the same way as convective storms.
Frontal storms may cover an extensive area, and may occur day or night. These storms are generally electrically more active than convective storms.
Thunderstorms are composed of fundamental structural elements called cells. These cells vary in diameter from one to five miles. The structure of each cell is characterized by patterns of convective circulating currents, and the circulation in each cell is generally independent of surrounding cells in the same storm.
The life cycle of a cell can be divided into three successive stages usually lasting for several hours. The three stages are:
1. Cumulus Stage
2. Mature Stage
3. Dissipating Stage.
The chief distinguishing feature of the cumulus or building stage is the updraft throughout the entire cell. The speed of the updraft usually varies between a few hundred feet per minute, to several thousand feet per minute. During this stage, the updrafts are generally fairly uniform over a large area, and apparently do not give rise to turbulence of such severity as to be considered dangerous to aircraft in flight. The effect is to cause vertical displacement of the aircraft, but not with such abruptness as to cause aircraft failure. The temperature inside the cell is everywhere higher than the temperature of the air surrounding the cell at the same altitude. Although water droplets form within the cell, they are held in suspension by vertical air currents, and no precipitation normally falls out of the base of the cloud at this stage.
The mature stage of the thunderstorm is signified by rain from the base of the cloud. By this time the cell has usually attained a height of 25,000 feet or more, and the rain drops and ice particles have become so large that they can no longer be supported by the upward air currents. As precipitation falls, drag is exerted upon the surrounding air, giving formation of downdrafts. While these downdrafts occur, updrafts still exist giving rise to high shear currents. Although the downdrafts generally have lower velocity than the updrafts, they can still reach a velocity of several thousand feet per minute. Aircraft stresses caused by flying abruptly from a region of rising air currents to a region of falling air currents, or conversely, represent a serious threat to safety. Structural failure and resulting crash of the aircraft have frequently been the result.
The mature stage generally lasts from 15 to 30 minutes, while the life span of the cumulus stage is about 10 to 15 minutes. However, the thunderstorm is composed of several cells which continuously form and dissipate, so the life of the storm is usually much longer, and the area occupied by the storm is usually much greater than that of a cell. The mature stage is characterized by strong updrafts, strong downdrafts, intense gusts, heavy rain, hail, strong surface winds, turbulence, and electrical activity. The thunderstorm is most active in all respects during the mature stage. It is this correlation between storm activity and electrical activity during the mature stage that forms a basis for storm mapping and avoidance through distant measurement of signals radiated by the electrical activity.
As the cell progresses, the entire lower levels become an area of downdrafts, and vertical motion soon ceases in the upper levels. Soon there is a downward current throughout the entire cell and the rate of rainfall decreases to that of a steady shower. This is the final or dissipating stage of the thunderstorm cell.
During the cumulus stage of the thunderstorm, through a process not fully understood, a separation of electrical charge occurs. Commencing with the mature stage, or perhaps during the latter portion of the cumulus stage, electrical discharges and lightning develop. As a matter of note, the occurrence of electrical discharges and lightning coincides with the occurrence of dangerous turbulence and other violence.
Each lightning stroke begins with a weakly luminous predischarge called the leader. The leader seems to prepare the way for a more powerful surge of current called the return stroke. Each lightning flash as observed by the eye, is usually composed of several strokes in rapid succession. Following the flash, the cell "rests" for a while before generating another flash. However, since a storm typically is composed of clusters of cells that are in various stages of activity, the group of cells may produce many lightning flashes per second.
Prior to the first lightning stroke, a low current discharge ionizes the air by moving rapidly in small intermittent steps. This first leader is called the stepped leader. The current in the stepped leader rises to the peak value in less than one microsecond then decays until the next step. The time interval between steps is about 50 microseconds. The stepped leader lasts for about 20 milliseconds, and during this time an average current of about 100 amperes flows.
Immediately after the ionized path has been prepared by the step leader, an intensely luminous return stroke propagates between the charge centers. This return stroke travels in a direction opposite from the direction of travel for the leader. The current in the return stroke rises at a rate of about 10 kA/.mu.sec, reaching a peak value of about 19,000 amperes in about 2 microseconds. The current slowly decays to one-half the peak value in about 40 microseconds. Currents of a few hundred amperes may continue to flow for several milliseconds.
The equation frequently used to express the current of the return stroke is: EQU i(t) = i.sub.0 (e .sup.-.sup..alpha..sup.t - e .sup.-.sup..beta..sup.t)(1)
where,
i.sub.0 = 28,000 amperes PA1 .alpha. = 4.4 .times. 10.sup.4 sec.sup.-.sup.1 PA1 .beta. = 4.6 .times. 10.sup.5 sec .sup.- 1 Equation (1) gives a peak current of 19,000 amperes, occurring at 5.6 microseconds. The time from peak to half value is 20 microseconds, somewhat less than the observed average value of 40 microseconds. Although not precise, equation (1) is a sufficiently good representation for many analytical purposes. PA1 H = Magnetic Field Intensity (amperes/meter) PA1 .epsilon..sub.o = Permittivity (farads/meter) PA1 c = Velocity of Light (meters/second) PA1 d = Distance from Discharge (meters) PA1 M = Total Electric Dipole Moment (coulomb-meters) (effective summation of each charge dipole moment)
The lightning flash is the total discharge, whereas the stroke is a component part of the total discharge. Each flash has an average of four strokes, however flashes have been observed having as few as one stroke, and as many as 26 strokes. As mentioned before, the first stroke is preceded by a stepped leader. After the first stroke, if the continuing current lingers long enough, another stroke can occur without a leader. But usually successive strokes will also be preceded by a leader, but for all but the first stroke, the leader is a "dart" leader. The dart leader differs from the stepped leader in that it travels smoothly. The time interval between strokes is typically about 40 milliseconds, and the time duration of the flash is in the order of 200 milliseconds. A typical representation of current versus time for a single flash is shown in FIG. 1.
The presence of electrical charge produces a static electric field in accordance to Coulombs Law. When charge is put in motion, additional fields are generated in accordance with Maxwell's Equations. The field strengths are commonly represented as: ##EQU1## where, E = Electric Field Intensity (volts/meter)
Brackets are used to indicate "retarded values" accounting for velocity of propagation.
For the electric field, the first term which is directly dependent upon the electric dipole moment, is referred to as the electrostatic field or coulomb field. This component is inversely proportional to d.sup.3. The second term depends upon the rate of change of dipole moment, or electric current, and is called the induction field. The induction field varies inversely as d.sup.2. The last term in equation (2) depends upon the second time derivative of the electric dipole moment, and is referred to as the radiation field or the far field. This field component is proportional to the acceleration of electric charge and is inversely proportional to distance. At distances greater than one wavelength, only the radiation field is of significance.
From equations (2) and (3), it is apparent that the E and H components of the radiation fields are always proportional to each other. Regardless of the waveform of the lightning discharge, these two field components remain proportional. Although not expressed by these equations, the E and H fields are vector quantities and propagate in space orthogonal to each other, and orthogonal to the direction of propagation. It is this property that permits an arrangement of sensors to derive azimuthal information as is common with RF direction finding techniques.
Prior to the first lightning stroke, many smaller sparks and minor electrical activity are observed. Then immediately prior to the stroke, the stepped leader appears. These processes prior to the return stroke emit weaker radiation primarily in the HF and VHF radio spectra. Radiation emitted by the return stroke occurs mostly in the LF and VLF spectra, is of great intensity, and can propagate over extreme distances.
Since the low frequency portion of the spectrum is generated by the return stroke, equation (1) can be used to determine the spectrum. The radiated fields will depend upon the derivative of the current waveform, and therefore the derivative of equation (1). By differentiating and taking the Fourier transform, break frequencies at .omega..sub.L = .alpha. and .omega..sub.H = .beta. are determined. Or, f.sub.L = 7 kHz and f.sub.H = 73 kHz. The spectrum will have the general shape illustrated by FIG. 2 with the amplitude diminishing below 7 kHz and above 73 kHz at a 6 DB/octave rate. This calculation agrees reasonably well with the averages of measured data.
Until relatively recent times, the most widely used method for storm location and avoidance was simply by visual means. Perhaps this is still the most widely used means. In the case of air travel, many lives have been lost while depending upon this method. Thunderstorms are frequently embedded in stratified layers of clouds, and are not visible. This is particularly true when storms are associated with the movement of a warm front. The appearance of cloud formations are frequently very deceiving. While flying at night, cloud formations are not observable.
Radar echoes can be produced by water droplets. This fact makes radar useful for storm mapping and avoidance. The presence of water droplets is most always associated with storm activity. Radar has been used very successfully simply by mapping areas of precipitation, and assuming that the edges of these areas correspond to areas of greatest turbulence.
There are certain limitations on the use of radar. Although this method has been very successful, detailed studies illustrate that precipitation and storm activity do not have a one-to-one correspondence. For example, moderate or even heavy precipitation can occur from stable weather formations. Also there have been many reports of extreme turbulence without precipitation. Then too, frozen water, hail, does not give radar reflections, yet this represents a dangerous form of weather.
Ground radar installations are widely used to advise aircraft pilots of unsafe weather formations. These are very useful, but do have additional limitations. When observing weather, the radar operator must select a particular form of polarization. The best polarization for weather, does not give good details for moving targets (aircraft). So when a ground radar assists a pilot with weather, he usually does so at the sacrifice of traffic control and advisories. The work load of the ground radar operator sometimes does not permit weather assistance.
Ground radar is also somewhat limited in range. If there are many cells, very dangerous weather formations can be hidden from view by weather formations in front. Then there are yet many areas not covered by radar service. And the coverage becomes more restrictive at the lower altitudes.
Airborne weather radar is perhaps the most useful and successful method of storm mapping and avoidance. In addition to the above-mentioned limitations, airborne radar is limited by its high cost. Also, airborne radar can only be installed in aircraft having space for the radome housing the antenna. This means that it is generally limited to multi-engine aircraft.
It has long been recognized that electric and magnetic fields from lightning strokes can be sensed and displayed on a CRT screen in terms of azimuth and sensed intensity. The method developed in England by Watson-Watt and Herd for finding the direction of atmospherics is illustrated in FIG. 3. Crossed loop antennas are used to sense the radiated magnetic field, and nondirectional sense antenna responds to the electric field. In the illustration, the lightning discharge is displaced in azimuth by the angle .theta.. The emf induced in the horizontal loop will be proportional to sin .theta., and the emf induced in the vertical loop will be proportional to cos .theta.. When these signals are amplified and used as deflection voltages for the CRT, a diagonal line is generated across the CRT, rotated by the angle .theta.. Since the deflection voltages are AC, the trace extends diagonally across the face of the CRT. If a wire antenna is used to sense the electric field, and if this signal is used for X-Axis blanking, half of the trace will be blanked. This happens because the electric and magnetic radiated fields are always in time phase. Since the loop antennas generate a voltage that is 90.degree. out of phase with the magnetic field, it is necessary to use a phasing network in the sense channel to correct for this. By blanking half of the trace, the ambiguity is eliminated, and a radial line is generated corresponding to the azimuth of the lightning discharge. The length of the line corresponds to the intensity of the received signal. The closer the lightning discharge, the longer the line. See, for example Andrews, U.S. Pat. No. 3,508,259.
This type direction finder has been used on the ground for mapping thunderstorms. It is simple and operates well. There are good reasons why this device has not been suitable for airborne mapping and storm avoidance. As mentioned before, the length of the line increases as the distance becomes less. Actually the device responds to intensity, but intensity is primarily influenced by distance. This type display gives the pilot a poor spatial concept of the storm's threat to his flight. Also, the display records transient phenomena, which further makes interpretation very difficult. When used on the ground, time exposure photographs were sometimes made to aid interpretation. Contemporary "long persistence" CRT screens do not provide the requisite storage time, and contemporary storage tubes are not economical. Summarizing, this type direction finder does not display data in a manner suitable for airborne use by an aircraft pilot.
Automatic Direction Finders (ADF) are in common use in aircraft. These direction finders receive broadcast signals and display the direction of the transmitting station relative to the aircraft heading. Usually indication is by a mechanical pointer. These direction finders make use of the electric and magnetic fields radiated by the transmitting station.
It has been observed that the ADF indicator will point to a thunderstorm. This is not too surprising as a lightning discharge is a powerful transmitter. This characteristic has sometimes been used by pilots in an attempt to avoid thunderstorms. The technique is, however, very unreliable for this purpose. There is no indication of intensity, nor is there anyway for the device to point to more than one storm location. If activity is from more than one location, an averaging will result giving completely wrong results. Also, the indicator is not suitable for storing the transient data. Following a stroke, the indicator is free to wander, or to be influenced by other signals. Then too, the operating frequency has been chosen for transmitting stations, and not optimized for thunderstorm detection.